Liquid Assets in Banks: Theory and Practice
Guillermo Alger and Ingela Alger
November 1999
Abstract
This paper summarizes theoretical ndings on the determinants of liquid assets held by
banks. The ndings are summarized in a series of predictions, some of which are tested
using a panel data set on Mexican banks. Surprisingly, we nd that banks with relatively
more demand deposits have relatively less liquid assets, in contrast with the theoretical
prediction. We further exploit a period characterized by a prolonged aggregate liquidity
shock on the Mexican banking system to shed light on the question: are there banks
that rely more than others on liquid assets to meet their liquidity needs? We nd that
only small banks seem to rely on liquid assets to meet severe liquidity shocks.
JEL Classication: G21; G28
Keywords: Liquid Assets; Banks; Liquidity Shocks
Analysis Group Economics (galger@analysisgroup.com) and Boston College (ingela.alger@bc.edu), respectively. We thank Jean Tirole, Esther Duo, Xavier Freixas, Denis Gromb, Sendhil Mullainathan and
Dimitri Vayanos for very useful comments and discussions. We are also grateful to Patricio Bustamante
and the Comision Nacional Bancaria y de Valores (Mexico) for the data set, and to several bankers and
regulators from the U.K., U.S. and Mexico for interesting discussions. This research was initiated while the
authors were visiting the Financial Markets Group at the London School of Economics, and we would like to
thank them for their hospitality, as well as for comments from FMG lunch seminar participants. We alone
are responsible for any remaining errors.
1 Introduction
The subject of this paper is liquid assets held by banks. Our objective is to provide a
comprehensive picture of this issue, by reviewing existing theory and empirical ndings,
and by providing some tests of theoretical predictions, using new data.
Broadly, the two main activities of banks are to accept funds through deposits and to
grant loans. A bank may however choose not to invest all its available funds in (typically
long-term) loans; indeed, it may keep some of the funds in cash (or reserves at the central
bank) and/or invest in marketable securities such as Treasury bills and bonds. The main
feature distinguishing these assets from regular bank loans is that they are more liquid. But
liquidity usually comes at a price, since liquid assets yield lower returns. A glance at banks'
balance sheets1 reveals that a substantial part of available funds are indeed invested in
liquid assets: adding up securities, dues from depository institutions, and cash, the average
holding of liquid assets in U.S. commercial banks in 1998 was 24.4% of total assets. Since
the returns are typically low, the question is: why do banks hold liquid assets?
Our analysis of this question begins with a review of existing theories, including those which
do not focus directly on how banks determine their level of liquid assets, but which do carry
implications for that. We distinguish four broad categories of theories. In the rst one,
the portfolio management theory developed in the 50's and 60's, risk aversion plays an
important role in explaining the level of liquid assets chosen by a bank. In contrast, all
other theories assume that banks are risk neutral. The second group of theories analyzes
the determinants of credit supply and deposit demand, viewing liquid assets as the residual
between, on the one hand, the bank's equity and liabilities, and on the other hand, the credit
portfolio. These two rst categories of theories do not explicitly take into account one of
the specicities of banks, namely, that they face potentially large, random liquidity shocks
(due to unpredictable deposit withdrawals, and or unpaid credits). Presumably, banks that
aim at staying in business wish to keep a good reputation concerning its ability to meet
liquidity demands. As a result, banks may want to keep liquid assets in order to be able to
1
See the appendix for a brief introduction to the items on a bank's balance sheet. For a detailed explanation, the reader may consult Garber and Weisbrod (1992) or Hempel, Simonson and Coleman (1994), for
instance.
meet large liquidity shocks, as suggested by the \liquid assets as a buer" theories. These
theories are however silent on one important question: to what extent may banks rely on
increased liabilities to raise liquidity on short notice (e.g., by selling CDs or borrowing from
other banks)? Indeed, these theories assume an exogenously given penalty rate if the bank is
not able to meet a liquidity need, without modeling the liability side of the bank's liquidity
management. This is an important shortcoming, since increased liabilities at rst sight
do appear as a cheap substitute for liquid assets: indeed, by relying on liabilities, banks
do not need to tie up important sums of money during long periods of time in order to
withstand occasional future shocks. Recent theories have started investigating the trade-o
between assets and liabilities to meet liquidity needs. These theories focus on information
asymmetries to explain a bank's limited borrowing capacity.
We summarize the theoretical results in a series of empirical predictions. We also make the
observation that most predictions relate to a bank's choice of liquid assets before a liquidity
shock occurs. In reality, banks face liquidity shocks every day, together with the decision
of how to invest in liquid assets for future needs, the net eect still being an unresolved
theoretical question. In our empirical analysis, introduced next, we exploit the fact that
our data covers a period with a dramatic liquidity shock to shed some light on the question:
can we distinguish banks that rely more on liquid assets to meet their liquidity needs than
others?
The empirical analysis rst provides tests of some of the theoretical predictions. We use a
panel data set for the Mexican banking system, from January 1997 to March 1999. Based on
the observation of several facts (tightening of monetary policy, political uncertainty related
to the banking system, and a strain on the Mexican economy due to a sharp decrease in the
oil prices and the worldwide nancial crisis in 1998), and comforted by econometric tests,
we are able to distinguish two periods: one characterized by \normal" conditions (January
1997-Fabruary 1998), and the second one characterized by an aggregate, prolonged liquidity
shock on the Mexican banking system (March 1998-March 1999). As a result, we use the
rst period to test the predictions concerning buer-building, and the second one to shed
some light on the above mentioned question, i.e., which banks rely more heavily on liquid
assets to meet their liquidity needs.
2
2 Review of Theoretical Findings
Before starting the review, it is necessary to provide a more precise denition of liquid assets. An asset is liquid if it can be sold quickly without signicant losses. What determines
the liquidity of an asset is still a disputed issue among theorists, and we will not review
that literature here.2 Instead, we will adopt the conventional wisdom found in the bank
management literature,3 an asset is liquid if it is widely known to have low risk (such as
government debt) and if it has a short maturity (a short maturity implies that the asset's
price is less sensitive to interest rate movements, making large capital losses unlikely). The
typical bank assets which are liquid according to that denition include cash, reserves representing an excedent as compared to reserves required by law4, securities (e.g., government
debt, commercial paper), and interbank loans with very short maturity (one to three days).
2.1 The portfolio management theory
According to Pyle (1971) and Hart and Jaee (1974), a bank's assets and liabilities may
all be viewed as securities. As a result of this interpretation, the whole bank may actually
be considered as a portfolio of securities. Once that view is postulated, it is possible to
apply the portfolio theory developed in the 50's and 60's to the asset-liability management
of a bank. The following simple model, adapted from Freixas and Rochet (1997, p.236)
illustrates the main ideas.
Assume for simplicity that there is only one risky nancial security (which may be interpreted as loans), and one risk-free security (the liquid asset), with returns r~L and r,
respectively. Starting with initial wealth E + D (equity and deposits, taken as an exogenously given amount here), the bank manager determines the amounts xL to invest in the
risky security, the rest being invested in the risk-free, liquid asset.5 A positive amount is
2
See the literature initiated by Kyle (1985), and also O'Hara (1995) for a review.
3
See Garber and Weisbrod (1992) and Hempel et al. (1994) for instance.
4
Indeed, reserves (i.e., funds held in the account at the central bank) are totally illiquid if they serve to
comply with a reserve requirement.
5
In this model, the bank manager is assumed to act fully in line with the bank owners objectives, i.e.,
there are no agency problems here.
3
interpreted as being on the asset side of the balance sheet, and a negative amount on the
liability side. Assuming for simplicity that the interest rate on deposits is zero, the random
payo is equal to:6
~ = r(E + D) + (~rL r)xL:
The bank manager is risk averse, and assumed to have mean-variance preferences: U (E (~); var(~)),
with U increasing in the expected prot, and decreasing in the variance. Given these
premises, the following result obtains: if the expected returns are ordered in the following
way, rL > r > 0 then xL > 0.
When it comes to the amount invested in liquid assets, E + D xL, the most important
determinant is risk, i.e., both the level of risk aversion, and the riskiness of the returns on
loans. First, E + D xL is increasing in the degree of risk aversion of the manager (for
low degrees of risk aversion, it may be negative). Hence, banks with relatively more liquid
assets should be more risk averse. Furthermore, for a given function U , and for given excess
returns (rL r), the amount invested in liquid assets is increasing in var(~rL), keeping rL
constant. An empirical implication is that, when the volatility of interest rates increases,
banks should decrease the amount of loans, and increase the holdings of liquid assets.
Another important implication of this theory is that, if deposits and equity are also interpreted as securities (i.e., if E and D are endogenized), then the size of the bank is
indeterminate. This follows simply from the fact that in that case, any multiple of the
portfolio which is optimal for a given level of equity and deposits, is also optimal. As a
result, size should be a random variable, and the proportion of liquid assets to total assets
should be independent of size.
2.2 Liquid assets as a residual: the role of supply and demand
The portfolio management theory of banking described above assumes that the bank manager is risk averse. Such an assumption could be defended for small, manager-owned banks.
6
In a more realistic model, the deposit interest rate would have to be determined endogenously. Here
that is disregarded, the focus being on the eect of risk aversion on the bank's balance sheet.
4
However, for banks owned by shareholders who have well-diversied stock portfolios, risk
neutrality seems to be a more appropriate assumption. Henceforth, risk neutrality is assumed. Given that the returns on liquid assets are typically lower than those on regular
bank loans, the question immediately arises of why any bank would invest in liquid securities
at all.
One way of dealing with the question is to view liquid assets as the dierence between equity
plus deposits and credits, and apply a classical microeconomic analysis of the determinants
of deposits and credits in terms of supply and demand (taking equity as given). This
contrasts with the portfolio management theory in which the supply of deposits and demand
of credits are perfectly elastic.
According to this theory, banks sell credit, using deposits as inputs. Accepting deposits
imply certain administrative costs, as does giving credits. These costs may be summarized in
two separate cost functions. If the demand for credit and supply of deposits are exogenously
given functions, then the standard marginal cost equals marginal revenue rule may be
applied to determine the amounts of credits supplied and deposits demanded by the bank.
From basic microeconomic analysis, we know that these will depend on the shape of the
cost functions and market structure. Thus for a given market structure, dierences in
balance sheet compositions could be traced to dierences in cost functions. As a bank's
cost functions are not observable by outsiders, it is however diÆcult to state meaningful
empirical implications using this approach.
A conceptually dierent determinant of credit supply is introduced when considering borrowers' default risk. Indeed, as shown by Stiglitz and Weiss (1981) and Bester and Hellwig
(1987),7 adverse selection or moral hazard may lead to credit rationing, in the sense that
there does not exist an interest rate for which the (competitive) market clears. For instance,
in the adverse selection case, an increase in the credit interest rate leads to a riskier population of borrowers, which in turn potentially implies a non-monotonic credit supply. If the
supply and demand curves do not intersect, credit is rationed. Compared to the competitive
outcome mentioned above, credit supply is smaller, and ceteris paribus, the investment in
7 Although
the models in these papers do not include banks' decisions to invest in liquid assets, we believe
the ideas exposed in them can be used to (partially) explain why a bank, for a given amount of deposits,
would limit its credits, thereby investing part of the funds available through deposits in liquid assets.
5
liquid assets should then be larger. An implication of that theory is that, given a level of
deposits, the liquid assets held by banks should increase if the population of borrowers is
believed to have become more risky, as could be expected during an economic recession for
instance.
2.3 Liquid assets as a buer
All the above mentioned models make an important simplication: they do not take into
account the unpredictability of deposit withdrawals, or other factors aecting the uncertainty of ows in and out of the bank, and the eects thereof. In contrast, a number of
researchers have sought to model the eects of the liquidity risk implied by these uncertainties. We review the insights concerning liquid assets, starting with models in which banks
invest in liquid assets for purely precautionary motives. That line of research was initiated
by Edgeworth (1888), and was further developed during the 1960's (see, e.g., Porter (1961),
and Kane and Malkiel (1965)).
A simple model, taken from Freixas and Rochet (1997, p.228), is useful to develop the
main insights. The two-period model features a bank deciding the amount x to invest in
liquid assets out of the funds available through an exogenously given amount of deposits
and equity, xD + E , the rest being invested in illiquid loans. Interest rates are given and
ordered as previously: rL > r > rD. A period after the investment decision, some deposits
are withdrawn and new deposits arrive; the net result is the realization w of the random
variable w~ (this is the only uncertainty in the model). If w exceeds the reserves x, the
bank suers a liquidity shortage; it must then pay a penalty rP (w x) (we will comment
further on the interpretation of rP below), where rP > rL. Assuming again for simplicity
that rD = 0, the objective of the bank is to maximize the expected prot:
(x) = rL(xD + E x) + rx rP E [max(0; w~ x)]:
The rst-order condition is:
0(x) = (rL r) + rP Prob[w~ x]:
6
This expression determines the optimal amount of liquid assets x as follows:8
Prob[w~ x] = rLr r :
P
The empirical implications are clear and intuitively appealing. First, the amount invested
in liquid assets decreases with the opportunity cost of investing in liquid assets, rL r.
Second, it increases when high values of w~ become more likely in the sense of rst-order
stochastic dominance. Note however that if the distribution of w~ becomes more risky in the
sense of second-order stochastic dominance, the eect on x is not clear; it could go either
way, depending on the exact shift in the distribution. Finally, it is increasing in the penalty
rate rP .
Several dierent interpretations of the penalty rate are possible. In a system where banks
can easily turn to the central bank for advances, it can be interpreted as the discount rate
(i.e., the rate charged by the central bank), which in such a system is typically higher than
other rates. In a system where such credits are not automatically given, it could be the rate
at which the bank may obtain funding on the nancial markets or the interbank market, or
the cost of liquidating illiquid assets.
In their model on why banks traditionally tie together the activities of deposit-taking and
lending, Kashyap, Rajan and Stein (1998) analyze a situation very similar to the one described above. The main dierence is that the expected deposit withdrawal is proportional
to the total amount of deposits. One prediction obtained in that paper is that banks with
relatively more demand deposits should hold relatively more liquid assets (an increase in
demand deposits corresponding to a shift in the shock distribution in the sense of rst order
stochastic dominance).
8 Again
risk aversion is not necessary for positive amounts of liquid assets to obtain. Nevertheless, the
amount of liquid assets would be aected by the introduction of deposit insurance. Indeed, deposit insurance
should lead banks to maximize risk, as shown by Merton (1977). Banks may however be interested in
investing in liquid assets despite deposit insurance, for instance in order to protect their charter value, as
suggested by Marcus (1984).
7
2.4 Liquid assets and liabilities: the role of market imperfections
The above mentioned approach does not explicitly model the liability side of a bank's balance sheet as a liquidity source. It is only implicitly present through the penalty rate. This
rate being exogenous and independent of the needed amount w~ x, the cost of increasing
liabilities (e.g., by issuing CDs, by borrowing from other banks or from the central bank)
is assumed exogenous, and the bank's access to these liabilities is not restricted. Recognizing the importance of liabilities as a liquidity source, Poole (1968) includes interbank
borrowings in a classical inventory model applied to banking. The model suggested by
Poole is however not entirely satisfactory, since it takes the supply of funds on the interbank market as perfectly elastic. The approach found in the recent literature seems more
promising in yielding new insights into the liquid assets question; in sharp contrast with
preceding theories, this approach seeks to explain why banks may only have limited access
to liabilities.
The market imperfections that have been studied are due to informational asymmetries.
Holmstrom and Tirole (1998) analyze the eects of moral hazard, whereas Lucas and McDonald (1992) focus on adverse selection.
In the model suggested by Holmstrom and Tirole (1998), rms (and therefore banks) encounter problems when raising external nance due to moral hazard (i.e., the manager
misallocates resources unless given proper incentives). Moral hazard implies that the bank
cannot pledge the full value of an investment project to outside investors. The bank makes
a long-term investment which may need extra funding at an interim stage due to a liquidity
shock. The crucial insight is that due to the moral hazard an ineÆcient decision may be
taken at that stage: indeed, there exist liquidity shocks which are small enough to make
further investment economically viable, but which are at the same time large enough to
make outside investors unwilling to invest (since they cannot recover the full value). A way
to avoid this ineÆciency is to invest in liquid assets beforehand, as this removes any need
to seek external nance at the critical interim stage. The authors determine the amount
of liquid assets chosen by the bank. Due to the linearity of the model, the only relevant
factor for the determination of the amount of liquid assets is the distribution of the liquidity
shock. When the distribution of the liquidity shock is riskier in the sense that larger shocks
become more likely overall (i.e., in the sense of rst-order stochastic dominance) the optimal
8
amount of liquid assets is larger.9 However, when the distribution of the liquidity shock
is riskier in the sense of a mean preserving spread (second-order stochastic dominance),
the optimal amount of liquid assets decreases. This results from the fact that when the
distribution is riskier in that sense, on the margin the investment in liquid assets implies
a lower increment of insurance: the achieved increase in the probability of continuation is
smaller than with the less risky distribution. Therefore, the bank \buys" less insurance,
and instead invests more in the illiquid project.10 11
Lucas and McDonald (1992) build on the insight of Myers and Majluf (1984) that private
information about asset quality aects a bank's (or more generally, a rm's) ability to
raise external nance.12 They consider a bank which may need external nance due to
a deposit shortcoming. As opposed to deposits, external nance is uninsured, and thus
sensitive to information about the bank's asset quality, which may be high or low. The
asset quality being private information, good and bad banks would pay the same rate for
external funding if they could not signal their quality (i.e., in a pooling equilibrium). Good
banks therefore have an incentive to signal themselves as good, and the signaling device
they use is the level of liquid assets. The intuition is as follows: while the benet of being
perceived as a good bank instead of a bad one is the same for both types of banks (through
the lower funding cost), the cost of investing in liquid assets is higher for the bad banks.
This follows from the fact that bad banks survive only if they receive a high return on
future loans: conditional upon surviving, bad banks therefore have a high average return
per unit invested. As a result, the opportunity cost of investing in liquid (low-yield) assets
is high. By contrast, a good bank survives even if the return on future loans is low. Hence,
conditional upon surviving, good banks have a lower average return per unit invested than
9
Note that this result again obtains in a model with only risk-neutral agents.
10
The above predictions are valid for banks' investments in securities, only insofar as stored liquidity is
preferred to credit lines. Indeed, as the authors point out, in their framework a perfect substitute for storing
liquid assets through securities is the negotiation of an irrevocable credit line up to the desired amount.
11
Rochet and Tirole (1996) propose an extension of this model, applied to interbank lending. They
analyze how peer monitoring aects the liquidity needs of lending and borrowing banks. Since the liquidity
shock structure is similar to the one in Holmstrom and Tirole (1998), the model yields similar predictions
concerning liquid assets.
12
The paper endogenizes the level of liquid assets (nancial slack), which was exogenous in Myers and
Majluf (1984).
9
bad banks, implying a lower opportunity cost. Therefore, good banks may signal themselves
by investing in liquid assets, and they nd that protable under certain conditions. The
model proposed by Lucas and McDonald thus leads to the prediction that, given a level of
deposits and a withdrawal distribution function, good banks should invest more in liquid
assets than bad banks.
2.5 Liquid assets and the interbank market
Last, we consider two papers that are concerned with interbank markets. Bhattacharya and
Gale (1987) and Alger (1999) analyze the role of interbank markets for the allocation of liquidity. In both papers, and in a similar vein to some of the above mentioned models, banks
choose the amounts to invest in liquid assets and in high-yield but illiquid loans, given that
there is uncertainty concerning the amount of deposit withdrawals before the loans mature.
Assuming away any aggregate uncertainty concerning the early deposit withdrawals, eÆciency (in the sense that there is not aggregate under-investment in loans) may be attained
through the existence of an interbank market: all banks choose the level of liquid assets
corresponding to the expected deposit withdrawal, and when the withdrawals realize, banks
with a liquidity shortage borrow from banks with a liquidity surplus. Bhattacharya and
Gale (1987) and Alger (1999) analyze two dierent potential sources of imperfection of the
interbank market, with dierent empirical implications.
Bhattacharya and Gale (1987) focus on the implications of asymmetric information about
the amount invested in liquid assets. If this amount is not observable to outsiders, a free
rider problem arises, implying that there is an aggregate shortage of liquidity when the
early deposit withdrawals occur. The authors suggest that reserve requirements could be
an answer to such a market failure.
Alger (1999) assumes that the amount of liquid assets is observable, and instead analyzes
an interbank market characterized by credit risk. At the time the banks seek additional
liquidity, they have private information about their solvency. The credit risk may lead the
interbank market collapse; hence in this framework, the interbank market is not always able
to provide liquidity insurance to banks, as it would without the adverse selection problem.
This aects the banks' investment in liquid assets, which is determined before banks know
10
whether they are solvent or not. If banks foresee that the interbank market will collapse,
they store a suÆcient amount of liquid assets to withstand large deposit withdrawals.13
In that case, there is over-investment in liquid assets compared to the situation in which
the interbank market functions properly. Furthermore, banks with relatively more equity,
having a higher stake at risk, invest relatively more in liquid assets.
The model also carries implications in terms of economic cycles. Indeed, the model incorporates the notion of correlation between the banks' returns. Thus, a high (resp. low)
probability that the bank is solvent combined with a high correlation between the banks'
returns, may be interpreted as an economic boom (resp. recession). The results of the
model thus indicate that the risk of an interbank market collapse is greater during economic recessions, or if the correlation between the banks' returns is highly negative. Thus,
if a recession is expected, banks should invest more in liquid assets.
2.6 Summary of predictions
Before turning to the empirical evidence, we summarize the predictions obtained through
the above described theories.
Prediction 1 The relative amount of liquid assets increases when their opportunity cost
(i.e., the dierence in returns on loans and on securities) decreases.
Most of the above theories yield this prediction, which may at rst seem trivial.14 Interestingly, however, the prediction challenges the conventional wisdom that high levels of liquid
assets imply low returns. Indeed, due to technological15 and strategic16 dierences, the
13
In a sense, this is related to the models focusing on liquid assets as a buer; in the case of interbank
market collapse, the penalty rate rP of those models is innitely high.
14
Note that in a general equilibrium framework, the level of liquid assets chosen would in turn aect the
opportunity cost.
15
Examples include dierences in management quality, in credit analysis models used by the bank, and in
securities analysis.
16
For instance specialization of the loan portfolio in dierent sectors, or of the securities portfolio in
dierent instruments.
11
returns on both the loans and the securities portfolios may dier across banks. Therefore a
high level of securities does not necessarily imply a lower level of returns.17
Prediction 2 The relative amount of liquid assets is higher if larger liquidity shocks are
more likely in the sense of rst order stochastic dominance.
This intuitively appealing prediction obtains in the buer theory and in Holmstrom and
Tirole (1998). Now, when do larger liquidity shocks become overall more likely? An occurrence which immediately comes to mind is seasonal uctuations. For instance, all banks
face larger withdrawals before holidays. Also, banks lending to sectors aected by seasonal
patterns in their production (such as the agricultural sector) do experience larger withdrawals during certain months of the year. Furthermore, the level of deposits may aect
the expected liquidity shock. One may assume that banks that withdrawals are proportional to the level of deposits, as in Kashyap et al. (1998). In other words, more deposits
simply means that the distribution of withdrawals shifts to the right. Hence, given that
assumption:
Prediction 3 Banks with relatively more demand deposits have relatively more liquid assets.
The following prediction obtains in Holmstrom and Tirole (1998) and in Rochet and Tirole
(1996).
17
The following simple portfolio model (adapted from section 2.1) illustrates this. The bank has to
determine the amount xL to invest in loans, given a liability size E + D, the rest being invested in the
risk-free liquid asset. Suppose that the manager has the following specic mean-variance utility function:
U (E (~ ); var(~)) = E (~) 21 var(~). Letting var(~ ) 2 be the constant variance of the return r~L , we get:
U (E (~ ); var(~)) = r(E + D) + (~rL r)xL 21 2 x2L , giving the rst-order condition: xL = (~rL 2 r) . Hence,
the amount invested in the liquid asset (E + D xL ) is decreasing in its opportunity cost (~rL r). Now,
one bank (say bank A) may, for the reasons mentioned in the text, have higher returns than bank B both
on its security portfolio, and on its loans. Using a superscript to denote the individual bank: rA > rB and
rLA > rLB . Given this, it may well be that rLA rA < rLB rB , i.e., that the opportunity cost of investing in
securities is smaller in the more protable bank. Hence, banks with relatively more liquid assets need not
be the least protable.
12
Prediction 4 If large and small shocks become more likely, and average-sized shocks become
less likely (i.e., if a distribution of shocks is riskier in the sense of second-order stochastic
dominance), the amount of liquid assets decreases.
The intuition behind this is clear as well: when the distribution of shocks is aected in the
sense of second-order stochastic dominance, the marginal benet of investing in liquid assets
may become smaller (the probability that the liquid asset will enable the bank to survive a
liquidity shock becomes smaller when large shocks become more likely). An example of the
distribution of liquidity shocks becoming more risky in the sense of second-order stochastic
dominance, is an overall increase in the volatility of interest rates and foreign exchange
rates, for instance.
Prediction 5 The relative amount of liquid assets increases with the volatility of the returns
on risky assets (loans).
This obtains in two theories. First it is implied by risk aversion in the portfolio management
theory. Second, even if the bank is risk neutral, it follows from the credit rationing argument
developed by Stiglitz and Weiss (1981): if the credit seeking population is believed to have
become more risky, the bank should decrease its loans, and therefore increase its liquid
assets.
Prediction 6 The relative amount of liquid assets increases with the renancing cost.
The buer theory yields this prediction if one interprets the penalty rate rP as the renancing cost. Also, in Alger (1999) banks invest more in liquid assets if the interbank market
collapses, which can be interpreted as an innitely high renancing cost. This prediction
is thus related to the substitutability of liquid assets and liabilities: if liabilities are more
expensive, the bank should make a heavier use of liquid assets as a liquidity source.
Prediction 7 Banks should hold more liquid assets when the banking sector is expected to
suer from low returns.
13
This prediction, which obtains in Alger (1999), is related to the previous one, since low
returns in the banking sector may decrease the supply of funds on the interbank market,
implying a higher renancing cost. Thus, if a recession is expected, banks should invest
more in liquid assets in order to avoid expensive liabilities.
The next predictions relate the relative amount of liquid assets to balance sheet characteristics. The rst one is a result in Alger (1999).
Prediction 8 Banks with relatively more equity should invest relatively more in liquid assets, for a given liquidity shock distribution.
The intuition is that banks with more equity have more to lose if they are not able to
withstand liquidity shocks, and therefore benet more from investing in liquid assets.18
Prediction 9 Banks with high asset quality should have relatively more liquid assets.
Lucas and McDonald (1992) obtain this result in a model where good banks use liquid
assets as a signaling device.
Prediction 10 The relative amount of liquid assets should be independent of bank size.
This last prediction obtains in the portfolio management theory, under the assumption
that all balance sheet entries, including equity, can be viewed as securities. In that case,
any multiple of an optimal portfolio is also optimal, implying that the size of the bank is
indeterminate. In turn, this implies that the amount of liquid assets is independent of bank
size.
Nevertheless this prediction does not take into account several issues related to renancing
cost. Intuition suggests that large banks have better access to liability funding. First, we
18
Note, however, that the distribution of the liquidity shock might actually be related to the relative
amount of equity. Banks relying more heavily on deposits could face larger liquidity shocks (see prediction
3).
14
can argue that large banks are better known than small banks; for instance large banks may
be more closely monitored and there may be more information sources, e.g., stock prices.
Second, creditors may view large banks as less risky (too-big-to-fail argument) implying a
lower renancing cost. We will comment further on this in the empirical section.
We conclude this section by a general remark concerning some of the above predictions.
Many of them were derived in models where banks invest in liquid assets in order to meet
future liquidity shocks; in other words, in these models the decision to invest in liquid
assets is separated from the decision to use them to meet a liquidity shock. In reality, such
a separation is not easily done. Indeed, every day banks must deal both with immediate
liquidity needs (which are not perfectly predictable) and with planning for future liquidity
needs. It is therefore possible that opposing forces are at work simultaneously: the bank
may wish to sell securities in order to meet an immediate liquidity need, and at the same
time build up a buer of securities to withstand future liquidity needs. The net eect is not
trivial. In the empirical analysis below, we believe we are able to shed some light on this
question.
3 Empirical evidence
In this section we provide empirical evidence, by analyzing data on the Mexican banking
system, and by reviewing existing evidence from the U.S.. The data set is a panel of 27
monthly balance sheets, income statements and call reports for 32 Mexican banks.19 These
32 banks represent 98.4% of the systemwide value of total assets. It covers the period from
January 1997 to March 1999.
The benet of analyzing a developing country to study liquidity is that aggregate liquidity
shocks are more volatile than in developed ones, because investors' capital is more volatile.
Furthermore, in the data set we can distinguish two periods with quite dierent liquidity
conditions for the banking sector.
The rst period, from January 1997 to February 1998, is characterized by quite \normal"
19
The data set is published by the National Banking and Securities Commission. Most of it is available
on their web-site http://www.cnbv.org.mx.
15
conditions: although Mexico as a whole encountered economic problems during this period,
the banking system was not particularly constrained. In contrast, the period from March
1998 to March 1999 is characterized by three events that put a strain on the banking
sector. First, the monetary policy shifted from neutral to tight.20 Second, the banking
sector became a major political issue in Mexico: the opposition attacked the government
for its management of the deposit insurance corporation FOBAPROA during the 1994-95
crisis. As a result, the future of banking regulation became highly politicized and uncertain.
In particular, future government aid for banks in trouble became more unlikely, making the
banking sector a more risky investment. Third, as an emerging and oil-exporting economy,
Mexico was hurt by the severe crisis which hit other emerging economies in 1998,21 and by
the sharp decline in oil prices.22
These facts led us to believe that aggregate liquidity in the banking system might have
changed signicantly between the two periods. As we will see below, descriptive statistics
and econometric analysis give strong support to that belief. We will therefore interpret the
rst period (January 1997 to February 1998) as the initial (buer-building) period of the
theoretical models, and the second (March 1998 to March 1999) as the period in which
the liquidity shock occurs. Hence, we will use the rst period to test some of the above
predictions in Sections 3.1 and 3.2. Then, in Section 3.3 we use the data from the second
period to determine which banks eectively use liquid assets as a liquidity source in times
characterized by an overall liquidity squeeze.
20
In Mexico, each day the central bank determines the sum of the banks' balances in their central bank
accounts through dierent interventions (purchases and sales of government securities, repurchase agreements, credits, deposits, etc). If the sum is zero, the monetary policy is neutral. There is a zero reserve
requirement in Mexico; if a bank's balance is negative on average over a period of two weeks, it must pay
twice the CETES rate (the Mexican equivalent of T-Bills). During the period January 1997 to February
1998, the policy was neutral. Beginning in March 1998, the policy became tight, and remained so until (and
beyond) March 1999. On March 6 1998, the central bank created a \corto" (shortage) of 20 million pesos
(approximately USD 2 million). On July 22, it increased to 30 million pesos, and then to 50 on August 10,
to 70 on August 27, to 100 on September 10, to 130 on November 30, and nally to 160 million pesos on
January 12, 1999.
21
The crisis started in South-East Asia, and then spread, to culminate with Russia's debt default and the
LTCM crisis in September 1998.
22
The oil price decreased from USD 17.5 per barrel in October 1997 to USD 7.96 in September 1998.
16
3.1 Descriptive statistics and stylized facts
Table 1 provides descriptive statistics for the period January 1997 to February 1998. Before
proceeding to the predictions, we list a few stylized facts for the buer-building period, based
on the gures in Table 2. There we have divided banks into three groups according to their
size relative to the banking sector: a small bank represents less than 1% of the banking
system, a medium bank between 1% and 10%, and a large bank above 10%. According
to this denition, there are 32 small banks, 12 medium banks, and 3 large banks. Table 2
indicates that for some important items in the nancial statements, small banks are quite
dierent from large and medium banks.
To begin, small banks hold on average 42.9% of total assets in liquid assets (dened as
securities plus cash and short-term interbank loans), the gures for medium and large
banks being 20.8% and 18.2%, respectively.23 This is in line with previous results for U.S.
banks. Using quarterly data between 1992 and 1996, Kashyap et al. (1998) nd that the
median large bank held on average 27% of their assets in cash and securities; the gure for
the median medium-sized bank was 29%, whereas for the median small bank it was 35%.24
Similarly, Lucas and McDonald (1992) nd that in 1987, on average large U.S. banks held
29% of total assets in cash and securities, medium-sized banks 33%, and small banks 39%.
We therefore consider the following to be a stylized fact: on average, small banks hold more
liquid assets relative to total assets than large and medium banks.
Furthermore, we would like to draw the reader's attention to the following features of the
gures in Table 2. First, on average small banks have less core deposits relative to total
assets than large and medium banks. Core deposits are deposits for which banks do not pay
any interest. Table 2 shows that small banks hold 3.5 times less core deposits than large
and medium banks. Second, on average, funding cost is negatively related to size. Funding
cost is dened as the monthly average interest rate on all liabilities. The large dierence in
core deposits is certainly part of the explanation for the dierence in funding cost. Third,
on average small banks have a higher ratio of equity to total assets than large and medium
23
Note that this in turn implies that small banks have relatively less loans.
24
Kashyap and Stein (1998) divide banks into six categories instead of three, and again the holdings of
cash and securities relative to total assets decreases with size.
17
banks. Finally, on average large banks are more protable than small and medium banks.
For protability, we use the ratio interest expense over interest income.25
3.2 Empirical tests for the buer-building period
In this section we test some of the predictions stated in Section 2.6, using the data from
January 1997 to February 1998. We focus on Predictions 3, 6, 8, and 10. We do not have
enough information to test the other predictions. For Predictions 2, 4, 5, and 7, we would
need to know the banks' expectations about future liquidity shocks. For Prediction 1, we
would need the expected return on loans and securities. We comment on Prediction 9 at
the end of the section.
Thus, we want to analyze whether demand deposits, renancing cost, capital, and size are
signicant predictors of liquid assets. We use three dierent measures for liquid assets:
securities, cash, and the sum of them (that we call liquid assets). We construct a crosssection and time-series panel, with indices i and t representing bank and date, respectively.
With 32 banks and 14 months, we have 442 observations.26
We make three separate regressions: one for securities SECUit, one for cash (this measure
includes overnight interbank loans) CASHit, and one for liquid assets (the sum of securities
and cash) LAit, as a fraction of total assets.27 For deposits, we distinguish between demand
deposits DEPOit (which depositors may withdraw at any time) and time deposits TDEPOit
(which have a xed maturity). Although we only want to test for eects of demand deposits,
we include TDEPOit to control for other eects. The variable TDEPOit includes certicates
of deposits (CDs) and all other interest bearing deposits. For size, we use the bank's market
share (assets of the bank as a fraction of total assets of the system).28 We use funding cost
FCit as a proxy for renancing cost for lack of a better measure. Letting Kit stand for
capital, we regress the three equations below. To allow for dierences between banks that
25
Interest expense is the sum of interest paid on all interest-bearing liabilities, and interest income is the
sum of interest and fees earned on all the bank assets.
26
6 observations are missing.
27
All other variables are also scaled by total assets.
28 We
also ran the regressions using the logarithm of assets for size, and obtained similar results.
18
are not captured in the model (i.e., individual dierences due to variables outside the model,
like for instance degree of risk aversion, or managerial idiosynchracies), we include individual
eects i.
LAit = i + 1 DEPOit + 2 TDEPOit + 3 Kit + 4SIZEit + 5 FC + it
(3.1)
SECUit = i + 1 DEPOit + 2 TDEPOit + 3 Kit + 4 SIZEit + 5 FC + it
(3.2)
CASHit = i + 1 DEPOit + 2 TDEPOit + 3 Kit + 4 SIZEit + 5 FC + it
(3.3)
We run both random and xed eects regressions.29 The results are summarized in Table
3.
Test of Prediction 3: Looking rst at the random eects estimates (columns 1,3, and 5
in Table 3), we nd that demand deposits have a signicant negative eect on securities
and liquid assets, whereas they have no signicant eect on cash. This result contradicts
the theory (Prediction 3) suggested by Kashyap et al. (1998). Since there is a risk that
the random eects estimates are biased (see footnote 29, we next look at the xed eects
estimates (columns 2,4, and 6). They show the same pattern as the random eects estimates.
Moreover, the Hausman test results formally conrm that we cannot reject the hypothesis
that the random and xed eects estimates are dierent. We therefore conclude that we
may have established a causal relation between demand deposits and securities (and also
between demand deposits and liquid assets, as implied by the relation between deposits and
securities, and the fact that the coeÆcient for cash is very close to zero).30
29
Fixed eects amounts to viewing each i as an unknown parameter to be estimated. In contrast, with
random eects regressions, the individual eects are viewed as random (and captured by an individual
error term ui ), and thus the following model is actually regressed (using the rst equation as an example):
LAit = + 1 DEPOit + 2 TDEPOit + 3 Kit + 4 SIZEit + 5 FC + ui + it: Whereas the random eects
estimators are more eÆcient than the xed eects estimators, the random eects model suers from a
drawback, namely, that it assumes that the individual error term ui is uncorrelated with the other regressors
(the 's). If that assumption is violated, the estimators are biased. The xed eects model does not rely on
such an assumption, and is thus more robust, albeit less eÆcient (since the estimation of the i 's amount
to a loss of a large number of degrees of freedom).
30
From Table 2, we know that banks with high ratios of demand deposits to total assets tend to be large.
It might therefore be tempting to conclude that our result could be explained by invoking that large banks
(those with relatively more demand deposits) have easier access to liability markets because they are too
big to fail, and thus need less liquid assets. However, that would be wrong. Indeed, in the regressions we
19
How do we explain this result? The theory relies on the assumption that the volatility of
demand deposit withdrawals increases as demand deposits increase. The empirical result
suggests that this assumption may be unrealistic. There are two alternative assumptions
that would better t our result. First, it may be that the variance of withdrawals decreases
as the depositor population of a bank becomes more diverse, which is typically the case
for large banks. Since in our data set higher ratios of demand deposits to total assets
are observed for large banks, such an assumption would be compatible with the empirical
result. A second possibility is that banks actually consider demand deposits to be very
stable liabilities, i.e., which are not a source of large, unpredictable liquidity shocks. Thus,
given an increase in demand deposits, banks might tend to invest more in loans than in
liquid assets.
Although Prediction 3 was mainly stated for demand deposits, we think it might carry over
to time deposits. Time deposits have a xed maturity, implying that the bank knows in
advance when it will have to be reimbursed. However, time deposits made by large investors
are often rolled over. As a result, the bank faces uncertainty concerning the fraction of
investors who will roll over their time deposits at maturity. Since time deposits typically
represent a larger fraction of total assets than demand deposits,31 it could be argued that
time deposits in fact would be a more important source for liquidity shocks than demand
deposits. Prediction 3 would therefore imply that the coeÆcient for time deposits (2) be
positive. The estimates in Table 3 show that it is not signicant for liquid assets nor for
securities. However, it is signicant and positive (but small) for cash. This does not lend
full support to Prediction 3, but it does suggest that banks invest demand and time deposits
dierently. We conclude this discussion by noting that further empirical research would be
valuable to shed more light on the assumptions to be used in theoretical models concerning
the most signicant sources of liquidity shocks.
Test of Prediction 6: Our results suggest that when funding cost increases there is a
signicant shift in the composition of liquid assets (cash decreases and securities increases),
whereas the overall eect on liquid assets is not signicant.
control for size and for individual eects such as reputation on the interbank market.
31
For large, medium, and small banks in our data set, the fractions were on average 50%, 47%, and 42%,
respectively, from January 1997-February 1998 (see Table 2).
20
Recall that our measure of cash includes overnight interbank loans. The composition shift
can be explained by a substitution of both cash and interbank loans for securities. First,
it seems reasonable to believe that an increase in the funding cost is correlated with an
increase in returns on securities (reecting an overall increase in market interest rates).
The opportunity cost of holding cash having increased, it is intuitive that cash drop and
securities increase. Second, the theory proposed by Alger (1999) suggests that an increase in
funding cost could lead to a decrease the interbank market activity (due to credit rationing),
and as a result, securities should increase.
Test of Prediction 8: Capital has a signicant positive eect on securities and liquid assets
as a whole, in line with the prediction.
As intuition suggests, when more capital is at stake, the bank will invest more in liquid
assets for precautionary motives.
Test of Prediction 10: We nd no signicant eect of the variable SIZEit on any of the
measure we use for liquid assets.
This seemingly lends support to the prediction that liquid assets and size are unrelated.
However, the gures in Table 2, and the intuition developed above, do seem to suggest that
size matters. To further investigate this, we rst plot liquid assets against size (see Figure
1). We see that there are three clusters of banks, corresponding to small, medium and
large banks. The variance for large banks is small, whereas it is larger for medium banks,
and huge for small banks. This large variance may explain why no linear relationship is
found. Notice however that only small banks have very large holdings of liquid assets, giving
partial support to our intuition that small banks must rely more on liquid assets and less
on liabilities to meet liquidity needs, or to the intuition that small banks are more averse
to risk.
Prediction 9: The theory behind the prediction that liquid assets signal a high asset
quality was suggested by Lucas and McDonald (1992), who also provide an empirical test
of their theory, using U.S. annual data from 1985-1989. The hypothesis they test is that
holdings of liquid assets is a predictor for future loan performance. They regress the ratio
of non-performing loans to total loans on the lagged ratio of the sum of cash and securities
to total assets, and on another set of potentially relevant variables. The data gives support
21
to their hypothesis that banks with a higher asset quality have relatively more liquid assets.
Letting NPit stand for the ratio of non-performing loans to total loans as the proxy for asset
quality, we make a similar regression:
NPit = i + 1(LAit ) 1 + 2(Kit ) 1 + it
(3.4)
(LAit) 1 is the lag of liquid assets (securities + cash) and (Kit) 1 is the lag of equity (both
being scaled as a proportion of total assets). The results are summarized in Table 4. We
nd that the relation is not signicant for Mexican banks. We would like to interpret that
result with caution, however, due to a possible distortion of the data.32
3.3 Evidence on eects of a liquidity shock
As mentioned previously, a few facts led us to believe that the period March 1998-March
1999 was characterized by an aggregate and prolonged negative liquidity shock on the
Mexican banking system. To give formal support to this belief, we run regressions (3.1),
(3.2), and (3.3) using the whole dataset, and adding a dummy for each of the 27 months
to control for dierences in the constant term across months, in each regression. The
coeÆcients for the dummies, plotted in Figure 2, suggest a structural change occurring in
the thirteenth month (i.e., March 1998, as expected). We therefore use the period March
1998-March 1999 to analyze which banks (if any) use their liquid assets to meet their
liquidity needs.
Unfortunately, the theory we reviewed in Section 2 does not give many hints as to which
types of banks (if any) will use their liquid assets more than others in case of an aggregate
liquidity shock. We will therefore base our discussion below on the following intuitions.
Banks who use their liquid assets to meet liquidity needs relatively more than others, are
those banks that must pay the highest interest rates, or who simply cannot nd liquidity on
the liability side.33 A bank may be in that situation if it is known to have a bad asset quality,
32
After the 1994 crisis the government bought much of existing bad loans, making bad banks look better
in our data.
33
In Mexico, banks cannot sell loans.
22
or, as suggested by the intuition developed above, if it is small and relatively unknown to
other banks and investors.
We begin the analysis of the data by running regressions to analyze whether banks changed
their behavior signicantly during the period March 1998-March 1999 (labeled A, as in after
the liquidity shock) as compared to the period January 1997-February 1998 (labeled B). We
modify (3.1)-(3.3) to test if a structural change occurred. We run the regressions, using the
whole dataset, allowing for dierent coeÆcients for the variables during the two dierent
periods (see Table 5). The Chow tests reveal that coeÆcients jointly are signicantly different between the two periods. Hence, we can conclude that banks' strategy with respect
to liquid assets changed, possibly as a result of the aggregate liquidity shock.
To further anlayze the dierence, we regress equations (3.1), (3.2), and (3.3) using the data
from March 1998-March 1999 (see Table 7). Comparing Table 3 and 7 yields interesting
insights. First, we notice that all coeÆcients become smaller (in absolute value) during the
second period, and that there are even sign changes. Next, we study in detail some of the
changes.
For demand deposits, the xed eects coeÆcient estimate changes from -.65 to .51 for
securities, from .019 to -.36 for cash, and from -.71 to -.13 (not signicant) for the sum of
cash and securities. Regarding securities, there are two possible explanations: rst, banks
may decide to invest more of demand deposits in securities than before. This can be a
result of banks expecting an increase in the volatility of liquidity (due to the tightening of
monetary policy and the worsening economic conditions in Mexico). Another explanation
is that banks ration credit, due to the overall increase in interest rates. Second, it may be
that there is simply a strong positive correlation betweem demand deposits and securities
(i.e., they both increase or decrease over the period). To help us analyze this, we plot the
average ratios of demand deposits, liquid assets, securities, and cash for small, medium,
and large banks over time (see Figure 3).34 We see that demand deposits decrease over the
second period (albeit not very strongly), while securities decrease dramatically for small
banks, and slightly for large banks (for medium banks, they increase). Thus, the second
explanation could be the right one.
34
See also Tables 2 and 6 for the descriptive statistics.
23
The fact that demand deposits decrease over the second period may also explain the negative
coeÆcient for cash mentioned above. Indeed, Figure 3 shows that all banks increase their
cash holdings quite dramatically. This is probably explained by an increase in interbank
market activity (due to the liquidity shortage, interbank market rates should have gone up,
making interbank lending an interesting investment): indeed, the overall increase in cash
is very close to the shortage of liquidity sustained by the Mexican central bank during this
period.
For capital, the estimated random eects coeÆcient changes from .27% to -.19% for securities. Figure 4, which plots average capital and the three dierent measures for liquid assets,
indicates that medium banks decrease their capital while their securities holdings increase,
the pattern being the opposite for small and large banks.
Finally, we can use Figure 3 to determine whether there is a dierence between large,
medium, and small banks. A striking pattern emerges: whereas large and medium banks
actually increase their holdings of liquid assets (from 18.2% to 19.1% for large banks, and
from 20.8% to 29.4% for medium banks), it decreases for small banks (from 42.9% to 32.8%).
Small banks seem to have been particularly aected by the crisis starting in the Summer
of 1998 and culminating in the Fall (months 22 and 23). Table 6 and Figure 3 further
reveal that the increase in liquid assets is due to an increase in cash only for large banks,
and partly cash, partly securities for medium banks. Small banks decrease their securities
dramatically, and not their cash holdings (which actually increased on average). Thus, small
banks were the only ones who sold o a signicant part of their securities, lending support
to our intuition. In contrast, medium banks increased their holdings, whereas large banks
decreased it slightly. In other words, large and medium banks did not seem to have been
really aected by the aggregate liquidity squeeze.
4 Conclusion
The objective of this paper was to provide an overview of theoretical results concerning the
determinants of liquid asset holdings by banks, to test some of the theoretical predictions
using Mexican data, and to try and identify banks that rely more heavily on liquid assets
to withstand liquidity needs during a large, and prolonged liquidity squeeze on the banking
24
system. We would like to emphasize three of our results, focusing on their implications for
future research.
First, we nd that banks seem to treat cash (including interbank loans) and securities rather
dierently. In the main regression (see Table 3), often the coeÆcients on cash and securities
are of opposing sign. This is quite a striking result, that suggests that we can probably
not view cash and securities as close substitutes. This contrasts with existing theory, which
does not distinguish between cash and securities.
Second, surprisingly our data suggests that there is strong evidence that banks having more
demand deposits (relative to total assets), have less liquid assets (relative to total assets).
This contrasts with the theoretical prediction, and with previous empirical results on U.S.
banks. We explain our nding by noting that the banks having relatively more demand
deposits are large banks. Intuition suggests that large banks dier from small ones on two
crucial matters. First, they typically have a more diversied depositor population. Hence,
we question the assumption underlying the theoretical prediction, namely, that liquidity
shocks are proportional to demand deposits. Second, intuitively large banks have better
access to liabilities to meet liquidity needs: they are better known, and creditors have better
incentives to monitor large banks; they may also be considered as too big to fail, further
diminishing the risk perceived by investors. As a result, large banks should not need to rely
on liquid assets to meet liquidity needs as much as smaller banks. The positive correlation
between size and the ratio of demand deposits to total assets could thus be an explanation
to our empirical nding.
The third major result of our analysis gives support to the above developed intuition: indeed,
analyzing data from a period characterized by a prolonged aggregate liquidity squeeze on
the Mexican banking system, we nd that only small banks reduce their holdings of liquid
assets substantially, whereas medium and large banks actually increase their holdings.
These two conclusions suggest that more research (both theoretical and empirical) could be
done on the dierences between small and large banks. Finding more support for signicant
dierences in their behavior could indeed have important implications for the regulation of
banks.
25
Appendix
The following table shows a simplied bank balance sheet.
Assets (uses of funds) Liabilities (sources of funds)
Cash
Securities
Repos to resell
Interbank lending
Loans
Demand deposits
Time deposits (CDs)
Repos to repurchase
Interbank borrowing
Capital
- Securities: debt and money market instruments with dierent maturities.
- Securities sold under agreement to repurchase are fully collateralized loans. The bank sells
securities, and the buyer agrees to repurchase them at a certain price on a certain date.
The maturity is usually very short, often overnight. The dierence between the sale and
repurchase prices yields an implicit interest rate for the funds borrowed.
- Certicates of deposit, or CD's are deposits with a xed maturity, which may be very
short. Large investors may contribute to increasing the bank's liquidity on short notice
through CD's. CD's may or may not be negotiable, i.e., they may or may not be sold
further on a secondary market.
- Interbank loans are made on a short-term basis, mostly overnight or even intraday. The
terms are set over the phone, over electronic networks linking the banks, or through brokers.
The loans are unsecured, and they may not be sold. They include loans from the central
bank. The interest rate is xed by the central bank, which also determines borrowing
eligibility rules.
26
Table 1: Descriptive Statistics, Panel January-97 to February-98 (rst table), and Panel
March 1998-1999 (second table).35
N. obs Mean
January 1997-February 1998:
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
March 1998-March 1999:
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
35
Sdev Percentiles
25%
50%
75%
448
448
448
442
442
448
435
448
0.3512
0.2256
0.1254
0.0954
0.4382
0.2492
0.1843
0.0268
0.2176
0.2115
0.1358
0.1034
0.1979
0.2171
0.0535
0.0514
0.1700
0.0771
0.0355
0.0036
0.3134
0.0859
0.1663
0.0007
0.3100
0.1366
0.0744
0.0503
0.4603
0.1919
0.1913
0.0016
0.5100
0.3288
0.1701
0.1826
0.5625
0.3396
0.2147
0.0265
416
416
416
416
414
416
414
416
0.3066
0.1413
0.1654
0.0995
0.4296
0.2115
0.2240
0.0273
0.1820
0.1412
0.1381
0.0998
0.2015
0.1843
0.0872
0.0505
0.1800
0.0398
0.0657
0.2784
0.2784
0.0753
0.1806
0.0009
0.2600
0.1016
0.1250
0.4657
0.4657
0.1538
0.2106
0.0016
0.4100
0.1787
0.2322
0.5874
0.5874
0.2986
0.2923
0.0277
Source: National Banking and Securities Commission CNBV, Mexico. http://www.cnbv.org.mx.
27
Table 2
: Descriptive Statistics, Large Medium and Small Banks January 1997 to February 1998.36
No. obs
Mean
Stdev.
Min
Max
42
42
42
42
42
42
42
42
42
42
0.1829
0.1316
0.0512
0.1881
0.5006
0.0775
0.1517
0.1729
0.8078
0.7577
0.0467
0.0311
0.0222
0.0375
0.0657
0.0209
0.0289
0.0294
0.0730
0.0419
0.1100
0.0760
0.0181
0.1070
0.4090
0.0451
0.1161
0.1262
0.6626
0.6056
0.3400
0.2182
0.1230
0.2392
0.6279
0.1092
0.2339
0.2208
0.9576
0.8135
112
112
112
112
112
112
112
112
112
112
0.2085
0.0968
0.1117
0.1912
0.4677
0.1080
0.1727
0.0389
0.8806
0.7724
0.1268
0.0571
0.1041
0.1046
0.1171
0.1084
0.0346
0.0195
0.2019
0.0978
0.0300
0.0001
0.0042
0.0085
0.2811
0.0162
0.0999
0.0088
0.5094
0.4664
0.6000
0.3806
0.4932
0.3959
0.7106
0.4597
0.2532
0.0757
1.2643
1.0089
294
294
294
288
288
294
281
294
288
288
0.4297
0.2881
0.1413
0.0446
0.4176
0.3275
0.1938
0.0014
0.7468
0.5084
0.2187
0.2352
0.1511
0.0676
0.2300
0.2222
0.0595
0.0016
0.2273
0.2165
0.0100
0.0018
0.0002
0.0003
0.0022
0.0458
0.0394
0.0001
0.0913
0.0077
0.9000
0.8911
0.6939
0.2739
0.8894
0.9460
0.2830
0.0077
1.6051
0.9810
3 Large Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
8 Medium Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
21 Small Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
36
The market share to total assets is 0.51, 0.43, and 0.044 respectively. Source: CNBV (Mexico).
28
Table 3: regression results, January 1997-February 1998. *** Signicant at 10% condence
level; ** Signicant at 5% condence level; * Signicant at 1% condence level. Standard
errors in parentheses. The Hausman test tests the null hypothesis that ^RE = ^FE , where
^RE and ^FE are the vectors of coeÆcient estimates using, respectively, the random eects
and the xed eects regression model.
LA
LA(fe)
SECU
SECU(fe)
CASH
CASH(fe)
-0.7193*
-0.6268**
-0.6502*
-0.6517*
-0.0646
0.0192
(0.1989)
(0.2633)
(0.2016)
(0.2597)
(0.1469)
(0.2326)
0.0832
0.0826
-0.0547
-0.0629
0.1277*
0.1440*
(0.0563)
(0.0579)
(0.0557)
(0.0572)
(0.0483)
(0.0512)
Capital
0.1943**
(0.0892)
0.1872***
(0.1034)
0.2750*
(0.0896)
0.3078*
(0.1020)
-0.0487
(0.0695)
-0.1203
(0.0913)
Funding Cost
-0.1046
(0.1583)
-0.0829
(0.1661)
0.2800***
(0.1569)
0.2633
(0.1638)
-0.4028*
(0.1351)
-0.3457**
(0.1467)
Size
-0.2010
(0.5560)
1.7391
(1.6073)
0.2675
(0.5879)
0.8882
(1.5856)
-0.4957
(0.3426)
0.8630
(1.4201)
No. obs
R-sq: overall
480
0.27
480
0.024
480
0.219
480
0.189
480
0.038
480
0.004
Hausman test
p-values
1.9
0.8633
Deposits
Time Deposits
1.11
0.9532
29
3.54
0.6172
Table 4: Fixed-eects estimates for equation (3.4) January 1997 - March 1999. Standard
errors in parentheses.
Nonperforming loans
Liquid Assets
Capital
No. obs
1
1
-0.0148
(0.0364)
R-sq:
-0.0371
(0.0803)
484
30
within 0.001
between 0.011
overall 0.009
Table 5: Regression results (random eects), January 1997-March 1999. Standard errors
in parentheses.
LA
Securities
Cash
Deposits (B)
-0.5402
-0.4494
-0.1267
Deposits (A)
(0.1645)
-0.3216
(0.1567)
-0.2885
(0.1245)
-0.0694
(0.1688)
(0.1606)
(0.1278)
Time deposits (B)
0.0600
(0.0569)
-0.0207
(0.0555)
0.0797
(0.0422)
Time deposits (A)
0.0406
(0.0505)
0.0648
(0.0492)
-0.0256
(0.0375)
0.3753
0.2344
0.1456
(0.0739)
(0.0717)
(0.0551)
-0.0806
-0.0896
0.0145
Funding Cost (B)
(0.0729)
-0.4940
(0.0706)
-0.2759
(0.0544)
-0.2021
Funding Cost (A)
(0.1952)
-0.1104
(0.1903)
0.1007
(0.1447)
-0.2108
Size (B)
(0.1223)
0.4864
(0.4538)
(0.1190)
0.4446
(0.4137)
(0.0908)
-0.0614
(0.3587)
Size (A)
0.4598
0.5701
-0.2240
(0.4677)
(0.4260)
(0.3698)
847
0.13
847
0.19
847
0.058
113.77
90.86
10.98
0
0
0.0518
Capital (B)
Capital (A)
No. obs
R-sq
Chow Test
(test of equality of coeÆcients in A and B):
F-statistic
p-values
31
: Descriptive statistics, for large, medium and small banks, March 1998 to March 1999.37
Table 6
No. obs
Mean
Stdev.
Min
Max
39
39
39
39
39
39
39
39
39
39
0.1908
0.1045
0.0856
0.1995
0.4919
0.0793
0.1817
0.1679
0.7782
0.7313
0.0452
0.0281
0.0377
0.0310
0.0685
0.0202
0.0485
0.0333
0.0720
0.0401
0.1000
0.0489
0.0268
0.1429
0.3828
0.0527
0.1202
0.1198
0.6642
0.6598
0.2900
0.1661
0.1465
0.2512
0.6241
0.1144
0.2864
0.2055
0.9489
0.8093
104
104
104
104
104
104
102
104
104
104
0.2939
0.1109
0.1830
0.1922
0.5014
0.1009
0.2212
0.0424
0.8529
0.6823
0.1664
0.1033
0.1577
0.1052
0.1188
0.0972
0.0647
0.0192
0.2127
0.1187
0.0600
0.0001
0.0227
0.0054
0.2440
0.0323
0.1063
0.0141
0.5226
0.3676
0.6400
0.4823
0.6078
0.3911
0.6581
0.4325
0.3543
0.0802
1.3996
0.9542
273
273
273
273
271
273
273
273
271
273
0.3280
0.1581
0.1701
0.0499
0.3931
0.2725
0.2310
0.0015
0.8173
0.6006
0.1932
0.1595
0.1357
0.0607
0.2284
0.1931
0.0967
0.0017
0.1879
0.2144
0.0100
0.0001
0.0019
0.0001
0.0004
0.0270
0.0789
0.0001
0.0528
0.0069
0.9000
0.7439
0.7174
0.2266
0.8849
0.9617
0.4126
0.0096
1.5602
0.9240
3 Large Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
8 Medium Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
21 Small Banks
Liquid Assets
Securities
Cash
Deposits
Time Deposits
Capital
Funding Cost
Size
Prot
Loans
37
The market share to total assets is 0.50, 0.45, and 0.05 respectively. Source: CNBV (Mexico).
32
Table 7: Regression results, March 1998 to March 1999. Standard errors in parentheses.
LA
LA(fe)
SECU
SECU(fe)
CASH
CASH(fe)
-0.1308
0.1484
-0.0572
0.5165
-0.2489
-0.3671
(0.2008)
(0.2301)
(0.1697)
(0.2211)
(0.1455)
(0.1694)
0.0473
0.0401
0.1343
0.1247
-0.0875
-0.0882
(0.0557)
(0.0559)
(0.0523)
(0.0537)
(0.0399)
(0.0412)
-0.2803
-0.3107
-0.1916
-0.2843
-0.0346
-0.0257
(0.0810)
(0.0833)
(0.0744)
(0.0800)
(0.0581)
(0.0613)
Funding Cost
0.1453
(0.0785)
0.1256
(0.0775)
-0.0733
(0.0754)
-0.1007
(0.0745)
0.2223
(0.0561)
0.2242
(0.0571)
Size
0.2707
(0.5912)
6.6671
(1.4033)
-0.1414
(0.4167)
6.2378
(1.3484)
0.0939
(0.4421)
0.3377
(1.0332)
No. obs
412
412
412
412
412
412
R-sq
0.07
0.12
0.08
0.16
0.06
0.07
Hausman test
35.63
0
Deposits
Time Deposits
Capital
p-values
50.14
0
33
3.46
0.6293
Figure 1: Liquid Assets and Size, January 1997-March 1999.
Panel January 1997 to March 1999.
.8
la
.5
.2
0
0
.05
.1
.15
size
34
.2
Figure 2: CoeÆcients of monthly dummy variables (for liquid assets, securities, and cash,
respectively), January 1997-March 1999.
.05
0
0
dla
dsecu
.05
-.05
-.05
-.1
-.1
0
6
13
month
20
27
0
6
13
month
20
27
.2
dcash
.1
0
-.1
35
0
6
13
month
20
27
Figure 3. Average demand deposits, liquid assets, cash, and securities by bank group.
ldepo
lal
ldepo
.24
lsecu
ldepo
.25
.25
.2
.2
.15
.15
lcash
.22
.2
.18
.1
.16
6
0
mdepo
13
month
20
27
.1
6
0
mla
mdepo
.35
13
month
20
27
6
0
msecu
mdepo
13
month
20
27
20
27
20
27
mcash
.3
.2
.25
.3
.15
.2
.25
.1
.15
.2
.1
.15
.05
6
0
sdepo
13
month
20
27
6
0
sla
sdepo
.6
13
month
20
27
6
0
ssecu
sdepo
13
month
scash
.4
.2
.3
.4
.2
.1
.2
.1
0
0
0
6
13
month
20
27
0
0
6
36
13
month
20
27
0
6
13
month
Figure 4. Average capital, liquid assets, cash, and securities by bank group.
lk
lla
lk
.25
lsecu
lk
lcash
.2
.2
.2
.15
.15
.15
.1
.1
.1
.05
.05
6
0
mk
13
month
20
27
.05
6
0
mla
mk
.4
.14
.3
.12
.2
.1
.1
.08
13
month
20
27
6
0
msecu
mk
13
month
20
27
20
27
20
27
mcash
.3
.25
.2
.15
6
0
sk
13
month
20
27
.1
6
0
sla
sk
13
month
20
27
6
0
ssecu
sk
.4
.4
.3
.3
.2
.2
13
month
scash
.5
.4
.3
.1
.2
0
6
13
month
20
27
.1
0
6
37
13
month
20
27
0
6
13
month
References
Alger, G., \A Welfare Analysis of the Interbank Market," mimeo, GREMAQ, Universite
des Sciences Sociales 1999.
Bester, H. and M. Hellwig, \Moral Hazard and Equilibrium Credit Rationing: An
Overview of the Issues," in G. Bambers and K. Spremann, eds., Agency Theory Information and Incentives, Springer Verlag 1987.
Bhattacharya, S. and D. Gale, \Preference shocks, liquidity and Central Bank pol-
icy," in W. Barnett an K. Singleton, ed., New Approaches to Monetary Economics,
Cambridge: Cambridge University Press 1987.
Edgeworth, F.Y., \The Mathematical Theory of Banking," Journal of the Royal Statistical Society, 1888, pp. 113{127.
Garber, P. and S. Weisbrod, The Economics of Banking, Liquidity, and Money, Lex-
ington, MA: D.C. Heath and Company, 1992.
Hart, O. and D. Jaee, \On the Application of Portfolio Theory of Depository Financial
Intermediaries," Review of Economic Studies, 1974, 41, 129{147.
Hempel, G.H., D.G. Simonson, and A.B. Coleman, Bank Management: Text and
Cases (4th ed.), New York:
John Wiley and Sons, 1994.
Holmstrom, B. and J. Tirole, \Private and Public Supply of Liquidity," Journal of
Political Economy, 1998, 106, 1{40.
Kane, E.J. and B.G. Malkiel, \Bank Portfolio Allocation, Deposit Variability, and the
Availability Doctrine," Quarterly Journal of Economics, 1965, 79, 113{134.
Kashyap, A. and J. Stein, \What does a Million of Observations on Banks Say about
the Transmission of Monetary Policy?," mimeo, University of Chicago and MIT 1998.
, R. Rajan, and J. Stein, \Banks as Liquidity Providers: An Explanation for the
Co-Existence of Lending and Deposit Taking," mimeo, University of Chicago and MIT
1998.
Kyle, A., \Continuous Auctions and Insider Trading," Econometrica, 1985, 53, 1315{1335.
38
Lucas, D.J. and R.L. McDonald, \Bank Financing and Investment Decisions with
Asymmetric Information about Loan Quality," RAND Journal of Economics, 1992,
23(1), 86{105.
Marcus, A.J., \Deregulation and Bank Financial Policy," Journal of Banking and Finance,
1984, 8, 557{565.
Merton, R.C., \An Analytic Derivation of the Cost of Deposit Insurance and Loan Guar-
antees: An Application of Modern Option Pricing Theory," Journal of Banking and
Finance, 1977, 1, 3{11.
Myers, S.C. and N. Majluf, \Corporate Investment and Financing Decisions When
Firms Have Information that Investors do Not Have," Journal of Financial Economics,
1984, 13, 187{222.
Poole, W., \Commercial Bank Reserve Management in a Stochastic Model: Implications
for Monetary Policy," Journal of Finance, 1968, 23(5), 769{791.
Porter, C., \A Model of Bank Portfolio Selection," Yale Economic Essays, 1961, Fall,
323{360.
Pyle, D., \On the Theory of Financial Intermediation," Journal of Finance, 1971, 26(3),
737{747.
Rochet, J.C. and J. Tirole, \Interbank Lending and Systemic Risk," Journal of Money,
Credit and Banking, 1996, 28, 733{62.
Stiglitz, J. and J. Weiss, \Credit Rationing in Markets with Imperfect Information,"
American Economic Review, 1981, 71, 393{410.
39